Solve by Addition/Elimination x+y=14 x=6y

$x + y = 14$ $x = 6 y$

Step 1

Subtract $6 y$ from both sides of the equation.

$x + y = 14, x - 6 y = 0$

Step 2

Multiply each equation by the value that makes the coefficients of $x$ opposite.

$x + y = 14$

$(- 1) \cdot (x - 6 y) = (- 1) (0)$

Step 3

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (x - 6 y)$ .

Apply the distributive property.

$x + y = 14$

$- 1 x - 1 (- 6 y) = (- 1) (0)$

Simplify the expression.

Rewrite $- 1 x$ as $- x$ .

$x + y = 14$

$- x - 1 (- 6 y) = (- 1) (0)$

Multiply $- 6$ by $- 1$ .

$x + y = 14$

$- x + 6 y = (- 1) (0)$

$x + y = 14$

$- x + 6 y = (- 1) (0)$

$x + y = 14$

$- x + 6 y = (- 1) (0)$

$x + y = 14$

$- x + 6 y = (- 1) (0)$

Simplify the right side.

Multiply $- 1$ by $0$ .

$x + y = 14$

$- x + 6 y = 0$

$x + y = 14$

$- x + 6 y = 0$

$x + y = 14$

$- x + 6 y = 0$

Step 4

Add the two equations together to eliminate $x$ from the system.

		$x$	$+$		$y$	$=$	$1$	$4$
$+$	$-$	$x$	$+$	$6$	$y$	$=$		$0$
				$7$	$y$	$=$	$1$	$4$

Step 5

Divide each term in $7 y = 14$ by $7$ and simplify.

Divide each term in $7 y = 14$ by $7$ .

$\frac{7 y}{7} = \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{14}{7}$

Divide $y$ by $1$ .

$y = \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$y = 2$

Step 6

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$x + 2 = 14$

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$x = 14 - 2$

Subtract $2$ from $14$ .

$x = 12$

Step 7

The solution to the independent system of equations can be represented as a point.

$(12, 2)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(12, 2)$

Equation Form:

$x = 12, y = 2$

Step 9

Solve by Addition/Elimination x+y=14 x=6y

Related Questions

Support LCMGCF.com by disabling your adblocker.